A-Level Discrete random variables: worked solution

Question

For the bag of 4 red and 6 blue balls, game two replaces each drawn ball before the next; a player makes 20 draws, recording each colour. Find the probability red is recorded exactly 4 times.

Each draw is with replacement, so P(red) = 4/10 = 0.4 is constant and draws are independent. Let X be the number of times red is recorded in 20 draws, so X ~ B(20, 0.4). P(X = 4) = C(20,4) (0.4)⁴ (0.6)¹⁶ = 4845 x 0.0256 x 0.00028211 = 0.0350 (3 s.f.).